Suppose That a Manufacturer Produces Two Brands of a Product

Suppose that a manufacturer produces two brands of a product, brand 1 and brand 2. Suppose the demand for brand 1 is thousand units and the demand for brand 2 is thousand units, where p₁ and p₂ prices in dollars. If the joint cost function is , in thousands of dollars, how many of each brand should be produced to maximize profit? ​

A) 74 units of brand 1
82 units of brand 2
B) 9 units of brand 1
52 units of brand 2
C) 74 units of brand 1
52 units of brand 2
D) 14 units of brand 1
38 units of brand 2
E) 27 units of brand 1
77 units of brand 2